Abstract: Let p be an odd prime,m be a positive integer,D be a positive integer with square free.In this paper the author proves that if p＞3,m＞1 and D is not divisible by p or primes of the form 2kp+1,then the equation x^p+2^mp=pDy² has no positive integer solutions (x,y) with gcd (x,y)=1.

Key words: higher diophantine equation, positive integer solution, existence